Simplify the expression. (−6 − 3i)(5 + 6i)

Distribute

-20 - 36i - 15i - 18i^2

-18i^2 - 51i- 36

Use foil to solve this problem.

Basically you want to multiply the second parentheses (5+6i) by the first parentheses (-6-3i). You can show this using the distributive method. Here's how it looks like:

-6(5+6i) - 3i(5+6i)

1. Distribute -6 inside the parentheses first.

(-30-36i) - 3i(5+6i)

*Here's something I think you should know: i times i (or i squared) is equal to negative 1.*

2. Now distribute -3i inside the parentheses.

To multiply -3i and 6i, you'll cancel the i values and make the i attached to the 6i become a -1, so now you have -3 times 6(-1), which is -3 * -6 = 18. This is why I have +18 in the second parentheses.

-30-36i - 15i+18

3. Remove the parentheses.

-30 - 36i - 15i + 18

4. Combine like terms.

-30+18 = -12

-36i-15i = -51i

-12-51i

Answer is:

-12 - 51i

answer for #1 is c

answer for #2 is d

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